Theoretical study on the effect of high Fe spin S = 5/2 on the organic two-dimensional electronic system of BETS compounds is made by the calculation with the mean-field approximation for the Coulomb interaction. It turned out that a relatively smaller value of on-site Coulomb interaction, U = U-BETS, On BETS sites compared with that of ET makes the nature of ground states sensitive to the band structure which are characterized by two different types of molecular arrangement, lambda- and kappa-type. The X-type system with a smaller band overlap shows a Mott-like insulating state, while the large band overlap of the kappa-type favors a nobel spin density wave (SDW)-like state newly found in our study. In both states, the spin amplitude is increased by the exchange interaction, J, between Fe spins and BETS electrons. Our results are summarized in the unified phase diagram, where at a fixed value value of UBETS close to the metal-insulator boundary, even a small value of J as well as the difference in the band structure changes the nature of state drastically. which fact is in accordance with the experimental reports, and the various ground states of the whole BETS family are explained within the same scheme.